1. ## Particle Motion

A particle moves on the X-axis so that its velocity at any time t is given by v(t)=sin2t. At t=0, the particle is at the origin.

a.) For 0<=t<= pi, find all values of t for which the particle is moving to the left
b.) Write an expression for the position of the particle at any time t.
c.) For 0<=t<=pi/2, find the average value of the position function determined in part (b)

a.) the particle is moving to the left from (pi/2,pi)
b.) p(t)=-.5cos(2t)+.5
c.) 2pi*the integral of sin(2t) from [0.pi/2]

is that all correct?

2. Originally Posted by ment2byours
A particle moves on the X-axis so that its velocity at any time t is given by v(t)=sin2t. At t=0, the particle is at the origin.

a.) For 0<=t<= pi, find all values of t for which the particle is moving to the left
b.) Write an expression for the position of the particle at any time t.
c.) For 0<=t<=pi/2, find the average value of the position function determined in part (b)

a.) the particle is moving to the left from (pi/2,pi)

correct

b.) p(t)= -.5cos(2t)+.5

correct

c.) 2pi*the integral of sin(2t) from [0.pi/2] no ...

$\displaystyle \textcolor{red}{\frac{2}{\pi} \int_0^{\frac{\pi}{2}} \frac{1}{2} - \frac{1}{2}\cos(2t) \, dt}$
.

3. Opps my mistake, thank you so much for pointing it out. I should read more carefully XD